I wanted to introduce some kind of gamification in my community and point system and badges seem to be the way to go for it. But as far as I know, the point system is not available in discourse and only badge system has been available to customize.
I would love to hear from someone if there is some working way to include point system in the forum otherwise I would like to know more about badges and how to configure them and more ideas on new badges.
No, Discourse does not a built-in “reputation”-style points system, beyond the trust level system which is a core component of how Discourse minimises spam and unpleasantness, and encourages trusted users to participate in moderating the site. I’m sure a plugin could be written (or one or more might exist already) to provide that, if it’s important.
As for badges, there is a lot of existing information on badges, how to customise them, and how to define your own custom badges, here on meta. A search will unearth them.